Efficient Rigorous Numerics for Higher-Dimensional PDEs via One-Dimensional Estimates

@article{Gameiro2013EfficientRN,
  title={Efficient Rigorous Numerics for Higher-Dimensional PDEs via One-Dimensional Estimates},
  author={M. Gameiro and J. Lessard},
  journal={SIAM J. Numer. Anal.},
  year={2013},
  volume={51},
  pages={2063-2087}
}
We present an efficient rigorous computational method which is an extension of the work Analytic Estimates and Rigorous Continuation for Equilibria of Higher-Dimensional PDEs (M. Gameiro and J.-P. Lessard, J. Differential Equations, 249 (2010), pp. 2237--2268). The idea is to generate sharp one-dimensional estimates using interval arithmetic which are then used to produce high-dimensional estimates. These estimates are used to construct the radii polynomials which provide an efficient way of… Expand
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